Study of the Optimal Waveforms for Non-Destructive Spectral Analysis of Aqueous Solutions by Means of Audible Sound and Optimization Algorithms
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applied
sciences
Article
Study of the Optimal Waveforms for Non-Destructive Spectral
Analysis of Aqueous Solutions by Means of Audible Sound
and Optimization Algorithms
Pilar García Díaz * , Manuel Utrilla Manso, Jesús Alpuente Hermosilla and Juan A. Martínez Rojas
Department of Signal Theory and Communications, Polytechnic School, University of Alcalá,
28871 Alcalá de Henares, Spain; manuel.utrilla@uah.es (M.U.M.); jesus.alpuente@uah.es (J.A.H.);
juanan.martinez@uah.es (J.A.M.R.)
* Correspondence: pilar.garcia@uah.es; Tel.: +34-918-856-733
Abstract: Acoustic analysis of materials is a common non-destructive technique, but most efforts
are focused on the ultrasonic range. In the audible range, such studies are generally devoted to
audio engineering applications. Ultrasonic sound has evident advantages, but also severe limitations,
like penetration depth and the use of coupling gels. We propose a biomimetic approach in the
audible range to overcome some of these limitations. A total of 364 samples of water and fructose
solutions with 28 concentrations between 0 g/L and 9 g/L have been analyzed inside an anechoic
chamber using audible sound configurations. The spectral information from the scattered sound is
used to identify and discriminate the concentration with the help of an improved grouping genetic
algorithm that extracts a set of frequencies as a classifier. The fitness function of the optimization
algorithm implements an extreme learning machine. The classifier obtained with this new technique
Citation: García Díaz, P.; Utrilla
is composed only by nine frequencies in the (3–15) kHz range. The results have been obtained over
Manso, M.; Alpuente Hermosilla, J.;
20,000 independent random iterations, achieving an average classification accuracy of 98.65% for
Martínez Rojas, J.A. Study of the
Optimal Waveforms for
concentrations with a difference of ±0.01 g/L.
Non-Destructive Spectral Analysis of
Aqueous Solutions by Means of Keywords: acoustic chemical analysis; non-destructive analysis; feature extraction; automatic classification
Audible Sound and Optimization
Algorithms. Appl. Sci. 2021, 11, 7301.
https://doi.org/10.3390/app11167301
1. Introduction
Academic Editor: Chiara Portesi Acoustic spectroscopy is one of the most promising techniques for nondestructive
testing of many materials. This work shows that acoustic spectroscopy in the audible range
Received: 8 July 2021
is also well prepared for the study of liquid solutions. No method can claim superiority,
Accepted: 6 August 2021
but sound-based sensing of liquids has several advantages over optical techniques and
Published: 9 August 2021
can be easily combined with other methods, such as electroacoustic measurements, as
discussed in [1]. A review devoted to describing the advantages and limitations of acoustic
Publisher’s Note: MDPI stays neutral
spectroscopy, with a particular focus on pharmaceutical applications can be seen in [2].
with regard to jurisdictional claims in
However, most studies on this research topic are devoted to ultrasound techniques
published maps and institutional affil-
and devices, due to their higher energy and bandwidth than sounds in the audible range.
iations.
This can be seen in the monographs devoted to this topic, like [3] and [4]. The last one is
very interesting because a research by Contreras et al. [5], page 51, describes the ultrasonic
measurement of different sugar concentrations with an accuracy of 0.2% in water volume
for pure sugar solutions. They measured the velocity of ultrasound and the density in
Copyright: © 2021 by the authors.
solutions of D-glucose, D-fructose, and sucrose at various concentrations (0–40% w/v) and
Licensee MDPI, Basel, Switzerland.
temperatures (10–30 ◦ C).
This article is an open access article
This conversion of acoustic data to sound velocity is the norm in most ultrasound
distributed under the terms and
studies of liquids. The calculation of sound velocities introduces some important problems
conditions of the Creative Commons
and uncertainties due to the need of using statistical or theoretical models and the existence
Attribution (CC BY) license (https://
creativecommons.org/licenses/by/
of other processes, as is explained in several publications, for example the Dzida et al.’s
4.0/).
excellent review about the determination of the speed of sound in ionic liquids [6]. A de-
Appl. Sci. 2021, 11, 7301. https://doi.org/10.3390/app11167301 https://www.mdpi.com/journal/applsci
Appl. Sci. 2021, 11, 7301 2 of 17
scription of a low-cost system for the measurement of sound velocity in liquids can be
found in [7].
The use of ultrasound for the study of pure liquids and solutions is limited, com-pared
to its application to colloids, suspensions, and emulsions, as reviewed in [8]. However,
there have been remarkable advances in recent years, as can be seen, for example, in [9–12].
The acoustic research of aqueous electrolytes was performed by Pal and Roy in [13] using
the Fourier spectrum pulse-echo technique, which is discussed in detail in [14].
The number of publications is too large for an exhaustive literature survey, so only a
handful of representative examples are shown here. For a detailed review of ultrasound
spectroscopy for particle size determination see [15]. In [16] Silva et al. studied polydisperse
emulsions by means of acoustic spectroscopy within the frequency range of (6–14) MHz in
order to measure the droplet size distribution of water-in-sunflower oil emulsions for a
volume fraction range from 10 to 50%. They concluded that the methodology was suitable
for polydisperse particle size characterization for moderate concentrations up to 20%
and the results were in good agreement with those obtained by laser diffraction analysis.
Other interesting application to food analysis can be seen in [17], where the mechanism
of rehydration of milk protein concentrate powders is studied by means of broadband
acoustic resonance dissolution spectroscopy. Moreover, ref. [18] describes the use of an
ultrasonic pulse echo system for vegetable oils characterization.
Good reviews of high-resolution ultrasound spectroscopy can be found in [19,20].
All measurements are based on the previous determination of the speed of sound and
attenuation in the samples. A number of advantages and applications of this technique are
clearly described, for example, samples with very small volumes can be analyzed using
different ranges of pressure and temperature. As is explained in [19], at frequencies below
100 MHz, which is clearly the case of audible frequencies, for nano-sized dispersions or
solutions, the contribution of scattering to attenuation can be neglected. Thus, attenuation
at this long-wavelength regime is determined by the thermal and the shear (visco-inertial)
effects. In spite of this, we show that audible acoustic spectroscopy can achieve impressive
accuracy in the determination of fructose concentration in water.
Another interesting application of ultrasound spectroscopy is the monitoring of bio-
catalysis in solutions and complex dispersions, even in real-time, reviewed in detail by
Buckin and Caras in [21]. The information that can be extracted from ultrasound data
is impressive: substrate concentrations along the entire course of the reaction, time pro-
file analysis of the degree of polymerization, reaction rate evolutions, kinetic mechanism
evaluation, kinetic and equilibrium constant measurements, and real-time traceability of
structural changes in the medium associated with chemical reactions, among others.
Finally, an interesting and fascinating application of audible acoustic measurements
can be found in [22,23]. Both deal on the determination of Martian rock properties using
the microphone of the recent NASA Perseverance rover. This microphone is used to record
the sounds associated with the microcrater-forming laser induced breakdown spectroscopy
device shots.
Additionally, artificial intelligence (AI) algorithms have been incorporated into many
engineering applications in recent years. They are integrated in research always providing
a remarkable improvement in performance and efficiency. The use of these algorithms
is enhanced by continuous and increasing computing power and massive data collec-
tion. Although they do not always offer the optimal solution, they approach it with a
very acceptable balance of cost and accuracy. Moreover, in many applications there is no
unique solution, but rather several solutions under conflicting criteria. Recent studies on
the application of IA in different fields of engineering can be found in: computer engi-
neering [24–27], electrical engineering [28,29], petroleum engineering [30], fluid mechanic
engineering [31,32], energy engineering [33–36], and acoustic engineering [37].
In this work a direct application of audible acoustic spectroscopy to the determination
of fructose concentrations in distilled water is presented. It is shown that no data conversion
to speeds of sound is necessary, hence eliminating the source of some uncertainty, and
neering [31,32], energy engineering [33–36], and acoustic engineering [37].
In this work a direct application of audible acoustic spectroscopy to the determina-
tion of fructose concentrations in distilled water is presented. It is shown that no data
conversion to speeds of sound is necessary, hence eliminating the source of some uncer-
Appl. Sci. 2021, 11, 7301
tainty, and most importantly, accuracies of the order of 1 part in 100,000 (0.001%) 3 of 17
in
weight can be achieved. The use of audible sound has some advantages over ultrasound,
mainly the low cost of the measuring equipment and the noncontact nature of the meas-
urements.
most In order
importantly, to optimize
accuracies theorder
of the technique,
of 1 parttheinresults
100,000from a series
(0.001%) of different
in weight can be pulses
achieved.
and noises The usepreviously
were of audible compared
sound has and somethe advantages
best soundover wasultrasound,
selected formainly
the finalthedeter-
low cost of the
mination. Thismeasuring
is a clear equipment
improvement andover
the noncontact
our previous nature of the measurements.
technique based on resonant In vi-
order to optimize the technique, the results from
brations of the sample, which involved direct contact [38]. a series of different pulses and noises
were previously
In this work, compared and the
364 samples of best soundconcentrations
different was selected for of the
highfinal determination.
purity fructose in dis-
This is a clear improvement over our previous technique based on
tilled water were used for the study of the best pulse characteristics for acoustic resonant vibrations of
chemical
the sample, which involved direct contact [38].
analysis. A constant volume of 150 mL for all samples was selected. The container was a
In this work, 364 samples of different concentrations of high purity fructose in distilled
simple cylindrical glass. A small anechoic chamber was used to place the samples and to
water were used for the study of the best pulse characteristics for acoustic chemical analysis.
make the sound recordings. The microphone was placed vertically over the surface of the
A constant volume of 150 mL for all samples was selected. The container was a simple
liquid. The
cylindrical sound
glass. source
A small was one
anechoic earpiece
chamber placed
was used parallel
to place to the microphone
the samples and to make over the the
liquid surface.
sound recordings. The microphone was placed vertically over the surface of the liquid. The
soundDifferent
source was sound configurations
one earpiece were explored:
placed parallel chirp, square
to the microphone overpulses, white
the liquid noise, and
surface.
maximum
Different length
soundsequence (MLS).
configurations In the
were end, MLS
explored: chirp,produced the best
square pulses, results
white noise,inand
our pre-
liminary studies
maximum and was(MLS).
length sequence selectedIn for
the the
end,final
MLSanalysis.
produced The
thesamples were
best results in excited
our prelim-by these
sounds during 30 s intervals and
inary studies and was selected for the reflected sound was recorded. These recordings were
final analysis. The samples were excited by these
sounds
divided during 30 ssamples
into 2-s intervalswhose
and thespectra
reflected sound
were was recorded.
calculated Theseof
by means recordings
the Praatwere program
divided
[39]. Theintoresulting
2-s samples whosewere
spectra spectra were calculated
processed by means by means
of a of the Praat genetic
grouping programalgorithm
[39].
The
(GGA)resulting
taking spectra wereset
a training processed
of 80% and by means
a test of
setaof grouping
20%. This genetic algorithm
algorithm (GGA)
provided a clas-
taking a training set of 80% and a test set of 20%. This algorithm provided
sifier with more than 98.5% classification accuracy, even for concentrations with a differ- a classifier
with
encemore thang/L.
of ±0.01 98.5% classification accuracy, even for concentrations with a difference of
±0.01 g/L.
2.2.Materials
Materialsand
andMethods
Methods
Theexperimental
The experimental system
system was
was composed
composed of three
of three main main parts:
parts: the anechoic
the anechoic chamber,
chamber,
the sound system, and the samples. The liquid sample was placed inside a small handmadehand-
the sound system, and the samples. The liquid sample was placed inside a small
made anechoic
anechoic chamberchamber
of exteriorofdimensions
exterior dimensions (width,
(width, high, depth) high,
80 ×depth) 80in× centimeters.
72 × 56, 72 × 56, in centi-
meters.
Its Itswas
interior interior was using
isolated isolated using
2-cm 2-cm
thick thick
foam andfoam and a frequency-dependent
a frequency-dependent absorbentabsor-
bent pyramidal
pyramidal material material
of 4 cmofin4the
cmbase
in theandbase
6 cmand 6 cm
high. high.
Thus, theThus, the volume
interior interior of
volume
the of
chamber is 58 is×58
the chamber 61×× 6140 cm.
× 40 AA
cm. cylindrical
cylindrical glass
glasswith
with a avolume
volumeofof200 200mLmLfilled
filledwith
with 150
150
mLmL of of a waterand
a water andfructose
fructose solution
solution was
wasplaced
placedatatthethe
center of the
center chamber.
of the The glass
chamber. The glass
mass
masswaswas123123g,g,with
witha diameter
a diameter of 8ofcm. Figure
8 cm. 1 shows
Figure 1 shows the schematic diagram
the schematic of theof the
diagram
experimental setup.
experimental setup.
Figure1.1.Photograph
Figure Photographof of
thethe experimental
experimental installation.
installation.
The proposed method uses differential measurements and the acoustic performance
of the chamber and the environment is sufficient for this purpose. Measurements of the
chamber performance were made by means of a Brüel and Kjaer 2250 acoustic analyzer,
resulting in 28.2 dBA of background noise and a mean reverberation time of 0.17 s. The
frequency response of the chamber is represented in Figure 2.
of theThe
chamber andmethod
proposed the environment is sufficient
uses differential for this purpose.
measurements and the Measurements of the
acoustic performance
chamber performance
of the chamber were
and the made by means
environment of a Brüel
is sufficient andpurpose.
for this Kjaer 2250 acoustic analyzer,
Measurements of the
resulting in 28.2 dBA of background noise and a mean reverberation
chamber performance were made by means of a Brüel and Kjaer 2250 acoustic time of 0.17 s. The
analyzer,
frequency response
resulting in of of
28.2 dBA thebackground
chamber is represented
noise and a in Figure
mean 2.
reverberation time of 0.17 s. The
Appl. Sci. 2021, 11, 7301 4 of 17
frequency response of the chamber is represented in Figure 2.
Figure 2. Frequency response of the anechoic chamber.
Frequency response
Figure2.2.Frequency
Figure response of
of the
theanechoic
anechoicchamber.
chamber.
The used microphone was the model ECM-TL3 of Sony, an electret capacitor with
The used microphone was theresponse
omnidirectional
The pattern, frequency
used microphone was the model
modelECM-TL3
range (20ofof
ECM-TL3 Sony, kHz)
Sony,anan
Hz–20 electret capacitor with
with sensitivity
electret capacitorofwith−35
dBomnidirectional
that was placed pattern, frequency
vertically 2.5 cm response range
over therange
liquid (20 Hz–20 kHz) with sensitivity of
omnidirectional pattern, frequency response (20surface,
Hz–20 kHz)1.5 cmwithfrom the center.
sensitivity In
of −35
−35 dB in
parallel, thata was placed vertically
symmetric position 2.5 the
to cm over
centertheofliquid
the surface,
glass, one1.5earpiece
cm from model
the center.Sony
dB that was placed vertically 2.5 cm over the liquid surface, 1.5 cm from the center. In
In parallel, in a symmetric
MDRXB50APB.CE7 was used position to the center
as thetosound source,ofofwith
the aglass, one earpiece
frequency response model
range Sony
of (4–
parallel, in
MDRXB50APB.CE7 a symmetricwas position
used as the the
sound center
source, the
with glass,
a one
frequency earpiece
response model
range Sony
of
24) kHz, a sensitivitywas
MDRXB50APB.CE7 of 106
used dB/mW,
as the and ansource,
sound impedancewith aoffrequency
40 ohms (1 kHz). The
response range testofsig-
(4–24) kHz, a sensitivity of 106 dB/mW, and an impedance of 40 ohms (1 kHz). The(4–
nals
24) were generated by a computer while the recordings were made by another computer
test signals were generated by a computer while the recordings were made by anothersig-
kHz, a sensitivity of 106 dB/mW, and an impedance of 40 ohms (1 kHz). The test
and
nals an
were external audiobycard.
generated a computer while the recordings were made by another computer
computer and an external audio card.
The
and anThe measuring
external system,
audiosystem,
measuring background
card. background sound, sound,and andnoise
noisesound
soundgenerated
generated byby
thethe sound
sound
card is
cardThe represented
measuringin
is represented in Figure
system, 3. A maximum
Figurebackground
3. A maximum level
sound,
level andof 0.0271 is measured
noiseissound
of 0.0271 generated
measured against
againstby the
thethe levels
sound
levels
near
near1is1(to
card (tofull
fullscale)
represented of
scale)in the
the signals.
ofFiguresignals.
3. A maximum level of 0.0271 is measured against the levels
near 1 (to full scale) of the signals.
Recordingof
Figure3.3.Recording
Figure of the
the sound
sound card
card without
withoutsignal.
signal.
Figure 3. Recording
The microphone of the
was sound card
connected to a without
PC soundsignal.
card MAudio Fast Track Ultra 8R. An
amplification factor of 70% for the channel was used to avoid adding internal noise from
the card. The measurements were taken with a recording rate of 44.1 kHz by means of the
free Audacity software [40]. Sound amplitude was kept below the 70% of the maximumAppl. Sci. 2021, 11, 7301 5 of 17
level in order to avoid saturation effects. Some test signals were generated by MATLAB [41]
and Audacity software:
1. MLS signal: a signal generated by MATLAB, taking into account that the maximum
length is 30 s. The amplitude is 60% of the full scale (FS);
2. White noise: a signal generated by Audacity, with an amplitude of 60% of the FS;
3. A set of chirp signals generated by Audacity, with a duration of 1 s each, from 150 Hz
to 15 kHz;
4. Square pulses with a period of 250 ms and 50% of duty cycle.
Each audio recording had a duration of 30 s, more than enough to ensure the precision
and stability of the measurements. Later analyses showed that the recordings were stable
enough to allow their partition in several 2 s intervals in order to increase the number of
recordings for the classification algorithm. Changes among different spectra from the same
sample were so low that they were not measurable.
The experiments were performed with a set of 364 samples of water solutions with
different concentrations of fructose (see Tables 1–3). The volume of each sample was
150 mL. Distilled water was used as solvent. Food grade pure fructose (>99%) was used for
the liquid samples. The concentrations of fructose were from 0 to 9 g/L. A more detailed
study was done between 2 g/L and 3 g/L in increments of ±0.1 g/L and between 2.01 g/L
and 2.09 g/L in increments of ±0.01, in order to explore the performance of the system. The
mass of fructose was measured by means of an analytical balance, a Homgeek TL-Series
balance with an accuracy of 50 g/0.001 g.
Table 1. Number of samples and their composition used in the experiment. A total of 130 samples of
distilled water with different concentrations of fructose, in the range of 0 g/L to 9 g/L, were analyzed.
Fructose Concentration (g/L) 0 1 2 3 4 5 6 7 8 9
Number of samples 13 13 13 13 13 13 13 13 13 13
Total samples 130
Table 2. Number of samples and their composition used in the experiment. A total of 117 samples
of distilled water with different concentrations of fructose, in the range of 2.1 g/L to 2.9 g/L,
were analyzed.
Fructose Concentration (g/L) 2.1 2.2 2.3 2.4 2.5 2.6 2.7 2.8 2.9
Number of samples 13 13 13 13 13 13 13 13 13
Total samples 117
Table 3. Number of samples and their composition used in the experiment. A total of 117 samples
of distilled water with different concentrations of fructose, in the range of 2.01 g/L to 2.09 g/L,
were analyzed.
Fructose Concentration (g/L) 2.01 2.02 2.03 2.04 2.05 2.06 2.07 2.08 2.09
Number of samples 13 13 13 13 13 13 13 13 13
Total samples 117
A set of 130 samples of water and fructose solutions with 10 concentrations between
0 g/L and 9 g/L, 117 samples of water and fructose solutions with 9 concentrations
between 2 g/L and 3 g/L, 117 samples of water and fructose solutions with 9 concentrations
between 2.0 g/L and 2.1 g/L have been analyzed inside an anechoic chamber using audible
sound configurations.
Samples were numbered and visual inspection was used in order to ensure that
complete dilution was achieved, and no bubbles were formed. Careful manipulation ofAppl. Sci. 2021, 11, 7301 6 of 17
the samples was done in order to avoid the formation of bubbles or wall drops. Each
measurement took 30 s and they were taken in a consecutive way.
Each measurement was divided into different 2-s intervals, after verifying that such
time was more than enough for accurate and precise spectral information. The input data
of the classification algorithm are the spectra of the audio measurements of 2-s in duration.
The experiment was carried out with one audio measurement of each of the 28 different
concentrations. That means a total of 364 audio samples. The power spectrum of every
interval was made using the default Praat 6.0.40 options as can be seen in our previous
work [38]. Similarly, a cepstral smoothing of 100 Hz and a decimation procedure were
applied (65,537 points); averaged in order to reduce the number of points to a reasonable
size (655 points) without losing the main peak structure of the spectra. In summary, the
classification algorithm processed 364 input data, each of them being a spectrum defined
by 655 values in the frequency range (20 Hz–22.05 kHz).
3. Algorithm for Clustering Problem
The spectral response of the liquid samples to the vibrational stimulation of the MLS
sounds was used as data input to a genetic grouping algorithm (GGA) to perform the
classification of the liquid mixtures according to their fructose concentration. Since the
nature of the samples was not affected, it is a non-destructive method. The GGA is itself
a genetic algorithm (GA) explicitly modified for solving clustering problems. A brief
description of GAs and GGAs is given in this section.
3.1. From Genetic Algorithm to Grouping Genetic Algorithm
GA is a bio-inspired algorithm based on the theory of evolution of species by natural
selection. A population of individuals fights against each other to gain the resources to
survive. Each individual represents an encoded solution of the optimization problem. It
is therefore an evolutionary optimization algorithm. The optimization strategy is usually
applied to solve problems where it is almost impossible to find the optimal solution and
there are several solutions with opposing criteria. The objective is to find one or multi-
ple solutions which are close enough to the optimal one, with a very acceptable balance
between cost and accuracy. On the other hand, “evolutionary” means that the algorithm
computes the solutions through successive generations, undergoing an evolutionary pro-
cess that enhances an overall improvement in the fitness value of the majority. Individuals
with better fitness values are likely to survive longer than individuals with worse fitness.
Along successive generations, individuals will appear that are more fit than others and
will progressively improve their fitness. Each generation of individuals undergoes changes
through recombination, mutation, and selection functions. These functions allow the diver-
sity of individuals and therefore the exploration of the solution space. The execution of the
evolutionary algorithm is completed when it reaches a stop condition. The most popular
stopping conditions are a maximum number of generations and population convergence.
Population convergence is reached when there is no progress in improving the fitness of
individuals over several consecutive generations. A more extensive introduction can be
found in [42].
The GGA is a modification of the GA oriented to solve grouping and clustering
problems [43–46]. The fundamental difference of a GGA versus a GA lies in the encoding of
the solution and the use of search operators to manage this encoding. The encoding is key
to ensuring high performance in the execution of the algorithm [47]. A solution in the GGA
is composed of two sections: the assignment part and the grouping part. The grouping
section labels all the groups involved in the solution. The assignment part associates each
element to a single group. The value stored in the assignment part is the group assigned to
each element. The information about the grouping is in the content of the solution itself
and in its length. The total length of the solution is the number of elements to be classified
plus the number of groups considered in the solution.Appl. Sci. 2021, 11, 7301 7 of 17
3.2. The Fitness Function: The Extreme Learning Machine
The fitness function numerically characterizes the individual and allows to rank the
individuals of a population from best to worst aptitude. The fitness function used in the
GGA is the extreme learning machine (ELM). It is a relatively simple machine learning
algorithm that generalizes a single hidden layer feedforward network (SLFN), used for
regression, binary classification, and multi-classification [48–53]. The input layer takes
the input values for a given set of features from the data. The feature set can include all
the features of the data or a subset of them. The output layer provides a classification
of the data according to the fixed feature set. The single intermediate layer is adjusted
by the training of the network. After training, the classification accuracy of the ELM is
calculated according to the defined feature set. ELM has demonstrated good performance
with extremely high speed [54–56]. This last feature is fundamental for its integration in
the GGA, since an extremely high number will be executed during each generation of the
evolutionary algorithm.
The fitness function is applied to an individual by calculating by ELM the classification
accuracy of each of the groups considered in the solution. The best rate is assigned as
the fitness value to the individual and the classification rates of the rest of the groups are
then discarded. The best classification accuracy corresponds to the group of features that
classifies the individual with the best accuracy among all the groups considered in the
solution. The rest of the groups are not relevant to the solution.
3.3. Metaheuristic GGA+ELM Algorithm Application for Spectral Analysis
As already mentioned, the spectral data have 655 values in the frequency range
(20 Hz–22.05 kHz). Obviously 655 characteristics is far too high for classification purposes.
The target of the optimization algorithm is to reduce the number of features useful for
classifying liquid samples. This means a wrapper feature selection [57] where the GGA
maximizes the classification accuracy. The solution is composed of a collection of features
varying in length and composition. The set of features extracted by the GGA among the
655 total will constitute the classifier applicable on the spectra of the liquid samples. The
challenge is to not exceed more than 10 features and to achieve a classification accuracy of
more than 95%.
The training and testing data sets are disjoint sets randomly selected from the total of
samples. The usual ratio is 80/20, with the training set having the largest number (80%) and
the test data the remaining 20%. The population size usually used in the literature varies
between 20 and 100 [58,59]. The pair composition of individuals for the crossover operation
is randomized. This method has also provided good results in previous research [60,61].
The crossover operation generates a population increase of 50% (a single offspring from
each pair), on which a 10% mutation is applied [47,59]. This percentage is higher than
usual in genetic algorithms, with the purpose of quickly exploring multiple areas of the
solution space. The survival population for the next generation is composed of the winners
of pairwise tournaments among the total population. The matches are chosen randomly.
The fitness function value of the fighters determines the winner of each tournament.
As already described, an individual is coded as a set of groups, where each group
is a collection of features that can be a valid classifier of the input data. Not all groups
of an individual are useful for classification, but only those with better accuracy. Note
that considering a specific individual, each feature of the 655 is only present in a single
group. In the GGA fitness function, the ELM algorithm is applied over each group of the
individual to classify the testing set data from the knowledge of the training data. The
group with the best classification accuracy is selected as a candidate classifier. The fitness
of the individual takes the value of the classification accuracy of this highlighted group,
which is the best accuracy obtained among all the groups of the individual.
The stopping condition employed in optimization is the maximum number of gener-
ations. To ensure the high-quality solutions are found within a reasonable computation
time, the maximum number of genera considered is Gmax = 50.best accuracy obtained among all the groups of the individual.
The stopping condition employed in optimization is the maximum number of gener-
ations. To ensure the high-quality solutions are found within a reasonable computation
time, the maximum number of genera considered is Gmax = 50.
Appl. Sci. 2021, 11, 7301 8 of 17
4. Results and Discussion
4. Results and Discussion
The spectral analysis was performed on a total of 364 spectra from 28 different fruc-
tose contents, having
The spectral 13 samples
analysis of each
was performed onconcentration. The 28
a total of 364 spectra concentrations
from have been
28 different fructose
contents, having 13 samples of each concentration. The 28 concentrations
grouped into three data tables with their respective fructose concentration increments: have been ±1
grouped
g/L in Tableinto
1, three dataintables
±0.1 g/L Tablewith their
2, and ±0.01respective fructose
g/L in Table concentration
3. The algorithmincrements:
was run on the
± 1 g/L in Table 1, ± 0.1 g/L in Table 2, and ± 0.01 g/L in Table 3.
three sample collections. One purpose of this work is to obtain a limited set of frequencies The algorithm was
run on the three sample collections. One purpose of this work
able to satisfactorily classify the samples according to their concentration. The main is to obtain a limited set ob-
of frequencies able to satisfactorily classify the samples according to their concentration.
jective is to determine the degree of discrimination of the classifier on fructose concentra-
The main objective is to determine the degree of discrimination of the classifier on fructose
tion using this method. It is expected that the accuracy classification of samples in Table 3
concentration using this method. It is expected that the accuracy classification of samples in
will
Table 3lower
be will bethan the
lower accuracy
than classification
the accuracy of samples
classification of samples in Table
in Table1, 1,asasininTable
Table 33 the
the con-
centration increment
concentration incrementis much
is muchlower
lowerthan
than inin
Table
Table1.1.ItItisisalso
alsodesired
desired to to know
knowwhether
whether the
accuracy classification of concentrations with a difference of ±0.01
the accuracy classification of concentrations with a difference of ±0.01 g/L is acceptable g/L is acceptable or not.
or not.
4.1. Acoustic Response Spectrum
4.1. Acoustic Response Spectrum
Figure 4 shows the averaged spectra for each concentration from Table 1. The spectra
Figure 4 shows the averaged spectra for each concentration from Table 1. The spectra
are defined by the sound pressure level (dB/Hz) over the audible frequencies range (20
are defined by the sound pressure level (dB/Hz) over the audible frequencies range
Hz–22.05 kHz). The sound pressure level is normalized in all the curves in Figure 4, with
(20 Hz–22.05 kHz). The sound pressure level is normalized in all the curves in Figure 4,
values in the in
with values range (−1–1).
the range (−1–1).
Figure 4. Cont.Appl. Sci. 2021, 11, x FOR PEER REVIEW 9 of 17
Appl. Sci. 2021, 11, 7301 9 of 17
Figure 4. Spectral information of the vibrational absorption bands of ten different concentrations
of fructose in distilled water (from 0 g/L to 9 g/L). The curves represent average and normalized
values of sound pressure level (dB/Hz) over the audible frequencies range (20 Hz–22.05 kHz) for the
Figure 4. Spectral information of the vibrational absorption bands of ten different concentrations of
samplesinfrom
fructose Tablewater
distilled 1. (from 0 g/L to 9 g/L). The curves represent average and normalized values
of sound pressure level (dB/Hz) over the audible frequencies range (20 Hz–22.05 kHz) for the sam-
Each spectrum can be characterized by particular markers associated with the chemical
ples from Table 1.
composition of the mixture. The selection of a group of frequencies manually as a classifier
of liquid mixtures from their concentration is a tedious and complex task because of the
largeEach spectrum
number can be
of spectral characterized
lines (the algorithmbyhandles
particularthe markers associated
range of audible with theaschem-
frequencies
ical composition
655 spectral lines).of the mixture. The selection of a group of frequencies manually as a
classifier
Theof liquid spectra
average mixtures from their
obtained withconcentration
the samples from is aTables
tedious and3complex
2 and also showtask because
a high
ofcomplexity.
the large number
Among of thespectral lines (the
mean spectra fromalgorithm handles
Table 3, with the range
increments ofg/L,
of 0.01 audible
somefrequen-
of
them
cies as are
655relatively similar to each other, and it may be necessary to select more focused
spectral lines).
frequency ranges to
The average discriminate
spectra obtainedone with
concentration from from
the samples another.Tables 2-3 also show a high
The optimization algorithm was run separately for
complexity. Among the mean spectra from Table 3, with increments each sample collection (Tables
of 0.01 g/L,1–3)
some of
them are relatively similar to each other, and it may be necessary to select morethat
providing several solutions. Each solution was composed of a set of frequencies focused
classify the samples with high accuracy. Two of these solutions were then taken to compose
frequency ranges to discriminate one concentration from another.
a combined decision system. This combined classifier works as a unique and common
The optimization algorithm was run separately for each sample collection (Tables 1–
classifier over all samples used. In the following lines, the performance of this classifier on
3)samples
providing
withseveral solutions.
concentrations from Each solution
Tables was composed of a set of frequencies that
1–3 is analyzed.
classify the samples with high accuracy. Two of these solutions were then taken to com-
4.2. Feature
pose Extraction
a combined decision system. This combined classifier works as a unique and com-
mon classifier over all
The GGA+ELM samplesperforms
algorithm used. Infeature
the following
extractionlines, the performance
optimizing the accuracyofclassi-
this clas-
fication
sifier of samples
on samples according
with to their fructose
concentrations concentration.
from Tables The genetic algorithm is fed
1–3 is analyzed.
with spectral information as shown in Figure 4. Each feature is a spectral line. The optimal
solution,
4.2. Featureif Extraction
it exists, is unknown. The algorithm delivers two of the best solutions found in
the execution. Each solution is composed of a set of frequencies (feature extraction) that
The GGA+ELM algorithm performs feature extraction optimizing the accuracy clas-
classify with high accuracy. Not all solutions have the same number of frequencies.
sification
A 2.7ofGHz
samples
Intel Coreaccording to their
i7 processor was fructose
used. Theconcentration. Thevalues
specific parameter genetic algorithm
of the GGA is
fed with spectral information as shown in Figure 4. Each feature is
and ELM are summarized below. Five independent simulations were performed for each a spectral line. The
optimal solution,
of the three sets ofif samples.
it exists, The
is unknown. Thesimulation
time for each algorithm was
delivers two of the1best
approximately h, sosolutions
the
found in the execution.
total computation Each
time was solution
about 15 h. is composed of a set of frequencies (feature extrac-
tion) that classify with high accuracy. Not all solutions have the same number of frequen-
cies.
A 2.7 GHz Intel Core i7 processor was used. The specific parameter values of the
GGA and ELM are summarized below. Five independent simulations were performed forAppl. Sci. 2021, 11, 7301 10 of 17
• Maximum number of generations = 50 generations;
• Training data size = 80%;
• Testing data size = 20%;
• Population size = 50 individuals;
• Mutation probability = 0.1;
• Number of neurons of ELM = 10 in Table 1; ELM = 11 in Tables 2 and 3.
No information on which frequencies to be tested first was given to the algorithm.
Table 4 lists the frequencies (kHz) of the independent classifiers. Classifier 1 consists of
4 frequencies in the range (8–15) kHz, and Classifier 2 selects five frequencies in the range
(3–15]) kHz. The two classifiers are combined into a single classification system. It is note-
worthy that with only nine features can characterize the 28 concentrations in Tables 1–3.
Table 4. Characteristics of the two classifiers provided by GGA+ELM to discriminate the fructose
concentrations of Tables 1–3. The classifiers make a decision according to the value of aver-age energy
density on specific frequencies in the acoustic response spectrum.
Frequencies (kHz) Classifier 1 Classifier 2
f1 8.4 3.1
f2 11.7 11.2
f3 13.8 12.8
f4 14.7 13.0
f5 - 14.5
4.3. Discussion
A total of 20 M random and independent iterations was run for the two independent
classifiers and the combined classifier on random test sets. The results are reported in
Table 5. For each set of concentrations (±1 g/L, ±0.1 g/L, and ±0.01 g/L) the average
value and standard deviation of the classification accuracy are given.
Table 5. Performance of the two classifiers provided by GGA+ELM and the voting system classifier
to discriminate the fructose concentrations referred in Tables 1–3. The average values and standard
deviation of the accuracy were estimated from 20 M independent and random iterations.
0–9 g/L (±1 g/L) 2.0–3.0 g/L (±0.1 g/L) 2.00–2.10 g/L (±0.01 g/L)
Classifier Average Standard Average Standard Average Standard
Accuracy Deviation Accuracy Deviation Accuracy Deviation
1 99.71 0.0126 90.32 0.0704 98.65 0.0272
2 97.60 0.0415 85.89 0.0727 80.78 0.0824
Combined
99.82 0.0123 98.98 0.0266 98.65 0.0272
classifier
Overall, it is observed that the combined classifier is valid for all concentrations in
Tables 1–3 (with a minimum average accuracy of 98.65% over the 20 M iterations). As the
average classification accuracy decreases, the difference between sample concentrations b
becomes smaller: 99.82% at ±1 g/L (Table 1), 98.98% at ±0.1 g/L (Table 2), and 98.65% at
±0.01 g/L (Table 3). The standard deviation also increases in this direction: 0.0123 with
±1 g/L (Table 1), 0.0266 with ±0.1 g/L (Table 2), and 0.0272 with ±0.01 g/L (Table 3). This
pattern meets the expected results: the difficulty of discrimination rises with higher class
similarity. In the following lines, we elaborate on the results for each set of classes (fructose
concentration), analyzing Tables 1–3 separately.
The classification of the samples of Table 1 (0–9 g/L) has very satisfactory results with
the three classifiers: Classifier 1 and 2 of Table 4 and the combined classifier of them. With
the three classifiers an average accuracy of more than 97% over 20 M random iterations is
obtained. It is very remarkable that Classifier 1 can characterize, with only four spectralThe classification of the samples of Table 1 (0–9 g/L) has very satisfactory results with
the three classifiers: Classifier 1 and 2 of Table 4 and the combined classifier of them. With
Appl. Sci. 2021, 11, 7301 the three classifiers an average accuracy of more than 97% over 20 M random iterations 11 of 17 is
obtained. It is very remarkable that Classifier 1 can characterize, with only four spectral
lines, up to ten concentrations with an average accuracy of 99.71%. Combining the two
lines, up to ten concentrations
decision-makers with anachieves
in a single classifier average an accuracy
average of accuracy
99.71%. Combining the 99.8%.
of better than two
decision-makers in a single classifier achieves an average accuracy of better than 99.8%.
The nine frequencies of the combined classifier are located in the range (3–15) kHz.
The nine frequencies of the combined classifier are located in the range (3–15) kHz.
These frequencies have been highlighted in Figure 5 on the spectral information of the
These frequencies have been highlighted in Figure 5 on the spectral information of the
vibrational absorption bands for each concentration of Table 1. Note that the combination
vibrational absorption bands for each concentration of Table 1. Note that the combination
of these spectral linesallows
of these spectral lines allowsthetheten
tenclasses
classes
to to
be be differentiated.
differentiated. NotNot all frequencies
all frequencies are are
equally
equally important in the classification operation, some frequencies are more decisive in the in
important in the classification operation, some frequencies are more decisive
the classification
classification among
among several
several classes.
classes. ThereThere
may be may be other
other sets ofsets of frequencies
frequencies that clas-
that classify
sify
the samples with similar accuracy. The optimization algorithm offers solutions close to theclose
the samples with similar accuracy. The optimization algorithm offers solutions
to the optimal
optimal solution,
solution, withoutwithout
ensuringensuring that
that there is athere is asolution.
unique unique solution.
Figure 5. Spectral
Figure 5. Spectral information
informationofofvibrational
vibrationalabsorption
absorption bands
bands of of
1010 concentrations
concentrations from
from 0 g/L
0 g/L to to 9
g/L. The curves represent the average and normalized values of the sound pressure level
9 g/L. The curves represent the average and normalized values of the sound pressure level (dB/Hz) (dB/Hz)
over
over the
the audible
audible frequencies range. In
frequencies range. In each
each spectrum, the frequencies
spectrum, the frequencies usedused for
for both
both classifiers
classifiers are
emphasized.
are emphasized.Appl. Sci. 2021, 11, x FOR PEER REVIEW 12 of 17
Appl. Sci. 2021, 11, 7301 12 of 17
Figure 6 shows ten different patterns for the concentration classification of Table 1.
Figure 6 shows ten different patterns for the concentration classification of Table 1.
Each pattern is constructed with the average normalized energy density value for each of
Each pattern is constructed with the average normalized energy density value for each of
the nine
the ninefrequencies
frequenciesatataaconcentration
concentration from
from Table
Table 1. The
1. The similarity
similarity between
between somesome patterns
patterns
is interesting. For example, the curve characterizing the 1 g/L concentration is similar to to
is interesting. For example, the curve characterizing the 1 g/L concentration is similar
the 55g/L
the g/L concentration
concentrationpattern.
pattern.The
The same
same happens
happens withwith
the the 4 g/L
4 g/L andand 9 g/L
9 g/L concentration
concentration
patterns.This
patterns. Thisphenomenon
phenomenon hashas been
been reproduced
reproduced in allin
theallexperiments
the experiments performed
performed and we and
we believe
believe that that it may
it may be associated
be associated with
with the the resonance
resonance of the container
of the container used. used.
Figure 6.6. Spectral
Figure Spectralinformation
informationpatterns
patterns forfor
fructose concentrations
fructose fromfrom
concentrations 0 g/L
0 to
g/L9 g/L, withwith
to 9 g/L, the the
average and normalized value of the sound pressure level (dB/Hz) as a function of the frequencies
average and normalized value of the sound pressure level (dB/Hz) as a function of the frequencies
(kHz)
(kHz) used
usedby bythe
thecombined
combinedclassifier.
classifier.
The application of the combined classifier on 143 samples from Table 2 (concentrations
The application of the combined classifier on 143 samples from Table 2 (concentra-
between 2.0 g/L and 3.0 g/L with increments of ±0.1 g/L) provided satisfactory results.
tions between 2.0 g/L and 3.0 g/L with increments of ±0.1 g/L) provided satisfactory re-
As in the previous case, a sequence of 20M random and independent iterations was carried
sults.As
out. Asshown
in the in
previous
Table 5,case, a sequence
Classifiers 1 andof 20M random
2 obtained and independent
an average iterations
accuracy higher than was
carried
85%, out. Astheir
whereas shown in Table
combined 5, Classifiers
classifier 1 and
improves the2 average
obtainedclassification
an average accuracy
accuracy higher
to
than 85%, whereas their combined classifier improves the average classification
98.98% with a standard deviation 0.0266. This result is very satisfactory, although worse accuracy
to 98.98%
than with a standard
that obtained for 1 g/Ldeviation 0.0266.The
concentrations. Thisgreater
result the
is very satisfactory,
similarity amongalthough worse
classes, the
than that
more obtained
complex for 1 g/L concentrations.
the classification and the lower the Theprecision.
greater the similarity among classes, the
moreFigure
complex the classification
7 presents the patternsandforthe
thelower the precision.
concentrations between 2.1 g/L and 2.9 g/L.
TheseFigure
have been generated
7 presents the from the average
patterns for the and normalized between
concentrations energy density
2.1 g/Lvalues for g/L.
and 2.9
the nine frequencies of the combined classifier. Very similar values are
These have been generated from the average and normalized energy density values forobserved in general
since the frequencies
the nine variation in ofconcentration
the combined is only ±0.1 g/L.
classifier. VeryExtreme closeness
similar values areisobserved
appreciatedin gen-
in some
eral sincecases such as the
the variation in2.3 g/L and 2.4 is
concentration g/L
onlyconcentrations, also with
±0.1 g/L. Extreme the 2.8isg/L
closeness and
appreciated
2.9 g/L concentrations.
in some cases such as the 2.3 g/L and 2.4 g/L concentrations, also with the 2.8 g/L and 2.9
g/L concentrations.Appl. Sci. 2021, 11, x FOR PEER REVIEW 13 of 17
Appl. Sci. 2021, 11, 7301 13 of 17
Figure 7. Spectral information patterns for fructose concentrations from 2.1 g/L to 2.9, with the average and normalized
Figure 7. Spectral information patterns for fructose concentrations from 2.1 g/L to 2.9, with the average and normalized
value of the sound pressure level (dB/Hz) as a function of the frequencies (kHz) used by the combined classifier.
value of the sound pressure level (dB/Hz) as a function of the frequencies (kHz) used by the combined classifier.
For classes with a concentration difference of ±0.01 g/L in Table 3, the 143 samples
wereFor
alsoclasses
analyzedwithbyaClassifiers
concentration
1, 2 anddifference
the combinedof ±0.01 g/L The
system. in Table 3, the 143
last columns samples
of Table 5
were
show also
theanalyzed by Classifiers
results obtained by each1,classifier
2 and the combined
over 20M random system.
andThe last columns
independent of Table
iterations.
5 Classifier
show the1,results obtained byineach
with 4 frequencies classifier
the 8–15 overand
kHz range 20M anrandom and independent
average classification itera-
accuracy
tions. Classifier 1, with 4 frequencies in the 8–15 kHz range and an
of 98.65% was much more effective than Classifier 2, where the accuracy de-creased to average classification
accuracy
80.78%. Theof 98.65% was much
combination of bothmore effective
classifiers than
did not Classifier
improve 2, whereofthe
the accuracy accuracy
Classifier 1, sode-
the combined
creased system
to 80.78%. considers
The only the
combination ofdecision of the firstdid
both classifiers classifier, ignoringthe
not improve theaccuracy
decision of
of the second
Classifier 1, so one. As discussed
the combined in theconsiders
system beginning of the
only thesection
decisionforof
thetheconcentrations of ig-
first classifier,
Table 1, not all frequencies contribute equally in the classification. At
noring the decision of the second one. As discussed in the beginning of the section for the the high similarity
concentrationsof
concentrations ofTable
Table 1,
3, the
not frequencies
all frequenciesof Classifier
contribute 2 doequally
not addinnew the information
classification.in At
the decision process over the information of Classifier 1. As a result, all
the high similarity concentrations of Table 3, the frequencies of Classifier 2 do not add the samples were
classified with an average accuracy of 98.65% and a standard deviation of 0.0272.
new information in the decision process over the information of Classifier 1. As a result,
The allocation of the four frequencies of Classifier 1 in the middle band of the spectrum,
all the samples were classified with an average accuracy of 98.65% and a standard devia-
between 8 and 15 kHz, is understandable. It is the band with high mean energy density
tion of 0.0272.
values. Figure 8 shows the position of these frequencies in the mean spectra of the nine
The allocation
concentrations of the2.01
between four frequencies
g/L of Classifier
and 2.09 g/L. Figure 9 shows1 in thethemiddle
patterns band of the by
generated spec-
trum, between 8 and 15 kHz, is understandable. It is the band with
Classifier 1 of the average and normalized energy density for the four frequencies. As high mean energy
density
in the values.
previousFigure
cases 8there
shows arethe
veryposition
similarofpatterns,
these frequencies
for example in the mean
in the spectra
2.01 g/L andof the
nine
2.02concentrations
g/L patterns. between
There is 2.01
also g/L and
close 2.09 g/L.between
similarity Figure 9the shows
2.03 the
g/L,patterns
2.05 g/L,generated
and
by2.09
Classifier 1 of the average and normalized energy density for the four frequencies. As
g/L patterns.
in the previous cases there are very similar patterns, for example in the 2.01 g/L and 2.02
g/L patterns. There is also close similarity between the 2.03 g/L, 2.05 g/L, and 2.09 g/L
patterns.Appl. Sci. 2021, 11, x FOR PEER REVIEW 14 of 17
Appl. Sci. 2021, 11, 7301 14 of 17
Figure 8.
Figure Spectralinformation
8. Spectral informationofofvibrational
vibrational absorption
absorption bands
bands of ten
of ten concentrations
concentrations fromfrom 0 to
0 g/L g/L to 9The
9 g/L. g/L. The curves
curves repre-
represent
sent the average
the average and normalized
and normalized valuesvalues
of theofsound
the sound pressure
pressure levellevel (dB/Hz)
(dB/Hz) overaudible
over the the audible frequencies
frequencies range.
range. In
In each
each spectrum,
spectrum, the frequencies
the frequencies used used for both
for both classifiers
classifiers are emphasized.
are emphasized.
Figure
Figure 9.
9. Spectral
Spectral information patterns for
information patterns for fructose
fructose concentrations
concentrations from
from 2.01
2.01 g/L
g/L to
to 2.09,
2.09, with
with the
the average
average and
and normalized
normalized
value of the sound pressure level (dB/Hz) as a function of the frequencies (kHz) used by the classifier
value of the sound pressure level (dB/Hz) as a function of the frequencies (kHz) used by the classifier 1. 1.Appl. Sci. 2021, 11, 7301 15 of 17
5. Conclusions
We have described a new non-invasive method based on the spectral analysis of
audible scattered sounds to conclude the concentration of liquid mixtures according to
their chemical composition with low cost. The spectral information was analyzed by a
metaheuristic algorithm. ELM was integrated to implement the fitness function of the
optimization algorithm GGA and extract a reduced set of frequencies as a classifier. The
acoustical response spectrum of the samples to MLS sounds was used after a previous
comparison with other sounds, like chirps, square pulses, and white noise. It was sufficient
to examine the spectrum response at a few frequencies instead of analyzing the whole
range of audible frequencies.
The experiments were carried out with 364 measurements from 28 samples of distilled
water and fructose mixtures (150 mL) with a fructose concentration varying between 0 and
9 g/L. The 28 concentrations were grouped into three sets with increasing difficulty: ten
between concentrations 0 g/L and 9 g/L with ±1 g/L increments, nine concentrations
between 2.1 g/L and 2.9 g/L with ±0.1 g/L increments, and nine between 2.01 g/L and
2.09 g/L with ±0.01 g/L increments.
This work has allowed us to reduce the problem to a set of only nine frequencies on
(3–15) kHz able to classify samples with concentrations of any of the three sets described.
In the most complex case, the proposed classifier was able to discriminate fructose concen-
trations with variations of ±0.01 g/L with an average accuracy of 98.65%. The higher the
concentration difference, the better the classification accuracy. For samples with increments
of ±0.1 g/L the average accuracy is 98.98%, and when the concentration increments are
±1 g/L, the average accuracy rises to 99.82%.
The optimization algorithm returned different solutions with similar performance.
The solution to the problem was not unique. It is important to note that changes in the
number of types are likely to change the set of frequencies selected in the solutions. Each
frequency had a different weight in the classification process. Future research will be
focused on analyzing other chemicals, more complex mixtures and improving the accuracy
of this sensing method.
Author Contributions: Conceptualization, J.A.M.R.; methodology, J.A.M.R., P.G.D., M.U.M. and
J.A.H.; software, P.G.D. and M.U.M.; validation, J.A.M.R. and J.A.H.; formal analysis, J.A.M.R., P.G.D.
and J.A.H.; investigation, J.A.M.R., P.G.D., M.U.M. and J.A.H.; resources, M.U.M. and J.A.M.R.;
data curation, P.G.D. and M.U.M.; writing—original draft preparation, J.A.M.R., P.G.D., M.U.M.
and J.A.H.; writing—review and editing, J.A.M.R., P.G.D., M.U.M. and J.A.H.; visualization, P.G.D.
and M.U.M.; supervision, J.A.M.R. All authors have read and agreed to the published version of
the manuscript.
Funding: No external funding sources were used for this research.
Institutional Review Board Statement: The study does not include research on humans or animals.
Informed Consent Statement: Not applicable.
Data Availability Statement: Data sharing not applicable.
Conflicts of Interest: The authors declare no conflict of interest.
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